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On Maximizing a Robustness Measure for Structured Nonlinear Perturbations
Maximizing Robustness Measure Structured Nonlinear Perturbations
2015/7/13
In this paper, we propose a robustness measure for LTI systems with causal, nonlinear diagonal perturbations with finite L_2-gain. We propose an algorithm to reliably compute this quantity. We show ho...
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
polynomial-time algorithm determining quadratic Lyapunov functions nonlinear systems
2015/7/13
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
Control Applications of Nonlinear Convex Programming
linear programming convex optimization interior-point methods robust optimal control
2015/7/10
Since 1984 there has been a concentrated effort to develop efficient interior-point methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important pro...
Efficient Nonlinear Optimization of Queueing Systems
Efficient Nonlinear Optimization Queueing Systems
2015/7/10
We present a systematic treatment of efficient nonlinear optimization of queuing systems. The suite of formulations uses the computational tool of convex optimization, with fast polynomial time algori...
Nonlinear Q-Design for Convex Stochastic Control
Convex optimization nonlinear control Q-parameter stochastic control
2015/7/9
In this note we describe a version of the Q-design method that can be used to design nonlinear dynamic controllers for a discrete-time linear time-varying plant, with convex cost and constraint functi...
A Batch Means Methodology for Estimation of a Nonlinear Function of a Steady- State Mean
Simulation Output Analysis Steady-State Simulation Nonlinear Estimation Batch Means Jack- knifing
2015/7/8
We study the estimation of steady-state performance measures from an Ad-valued stochastic process Y = {Y(t): t≥0} representing the output of a simulation. In many applications, we may be interested in...
User’s Guide for SNOPT Version 7: Software for Large-Scale Nonlinear Programming
optimization large-scale nonlinear programming nonlinear constraints
2015/7/3
SNOPT is a general-purpose system for constrained optimization. It minimizes a
linear or nonlinear function subject to bounds on the variables and sparse linear or
nonlinear constraints. It is suita...
A GLOBALLY CONVERGENT LINEARLY CONSTRAINED LAGRANGIAN METHOD FOR NONLINEAR OPTIMIZATION
large-scale optimization nonlinear programming
2015/7/3
The new algorithm has been implemented in Matlab, with an option to use either MINOS or
SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are
required...
Statistical Mechanics of a Discrete Nonlinear System
Statistical mechanics discrete nonlinear schrodinger equation the partition function
2014/12/29
Statistical mechanics of the discrete nonlinear Schrödinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of sta...
Wannier functions analysis of the nonlinear Schrödinger equation with a periodic potential
Walter's function nonlinear schrodinger equation periodic vector lattice
2014/12/29
In the present paper we use the Wannier function basis to construct lattice approximations of the nonlinear Schrödinger equation with a periodic potential. We show that the nonlinear Schrödi...
Instabilities and bifurcations of nonlinear impurity modes
Stability of nonlinear discrete impurity mode nonlinear schrodinger equation the discrete soliton discrete breathing
2014/12/29
We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schrödinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay betwe...
Breathers on a background: periodic and quasiperiodic solutions of extended discrete nonlinear wave systems
Discrete nonlinear wave equation the discrete sine Gordon a discrete nonlinear schrodinger equation the periodic oscillation kink
2014/12/29
In this paper we investigate the emergence of time-periodic and time quasiperiodic (sometimes infinitely long-lived and sometimes very long-lived or metastable) solutions of discrete nonlinear wave eq...
Modulational instabilities and domain walls in coupled discrete nonlinear Schrödinger equations
Discrete nonlinear schrodinger equation linear coupling plane wave coupling
2014/12/29
We consider a system of two discrete nonlinear Schrödinger equations, coupled by nonlinear and linear terms. For various physically relevant cases, we derive a modulational instability criterion ...
Parametric and modulational instabilities of the discrete nonlinear Schrödinger equation
The coupling instability discrete nonlinear schrodinger equation condensate dynamics
2014/12/29
We examine the parametric and modulational instabilities arising in a non-autonomous, discrete nonlinear Schrödinger equation. The principal motivation for our study stems from the dynamics of Bo...
On the Modulational Instability of the Nonlinear Schrödinger Equation with Dissipation
Space is unified nonlinear schrodinger equation the high order dissipation condensate
2014/12/29
The modulational instability (MI) of spatially uniform states in the nonlinear Schrödinger (NLS) equation is examined in the presence of higher-order dissipation. The study is motivated by result...